[en] We discuss the relativistic treatment of fermion-antifermion bound states by an effective Hamiltonian method which imitates description in terms of nonrelativistic potential models: the effective interaction potential, to be used in a Schroedinger equation which incorporates relativistic kinematics, is derived from the underlying quantum field theory. This approach is equivalent to the instantaneous approximation to the Bethe-Salpeter equation called Salpeter equation but comes closer to physical intuition than the latter one. We propose a new method for solving the spinless Salpeter equation. Choosing a special set of orthonormal basis functions we are able to calculate analytically the integral of the corresponding kernel as well as the matrix elements of a class of potentials. In this way the problem can be reduced to the solution of a simple matrix eigenvalue problem with explicitly known matrices, which can be solved very fast numerically. The method is demonstrated in detail for S waves using a typical interquark potential as example